DALLAS -- James Harden scored a career-playoff-high 42 points and the Houston Rockets withstood Dallas' desperate punch to beat the Mavericks 130-128 and take a commanding 3-0 series lead Friday night.

The Rockets can close out the best-of-seven playoff series and move on to the Western Conference semifinals with a victory Sunday night back at American Airlines Center.

Houston trailed by 13 in the first half before storming back behind Harden, an MVP candidate shooting guard who scored 16 in third quarter and knocked down a jumper with 13 seconds left that helped nail down the win.

Rockets center Dwight Howard pulled down a playoff career-best 26 rebounds and scored 13 points. His childhood friend, forward Josh Smith, had 18 points off the bench.

The Mavericks, buoyed by playing in front of their home fans for the first time in the series, now face the seemingly impossible task of winning four straight games to advance.

No team in NBA history has come back to win a series after falling behind 3-0.

The Mavericks had their chances in the final minute. Power forward Dirk Nowitzki (34 points) drilled three free throws with 34 seconds remaining to pull Dallas within 127-126.

Harden followed with his final basket before Dallas shooting guard Monta Ellis banked in a driving layup to make it a one-point game again. Rockets reserve guard Corey Brewer (15 points) made one of two free throws, giving Dallas one last shot.

Ellis, however, couldn't add on to the highest-scoring game of his playoff career as he missed a jumper from the top of the key as time expired. Ellis finished with 34 points on 15-of-25 shooting.

Dallas came in with two starters out due to injury, at least officially. Small forward Chandler Parsons is headed for knee surgery, but the saga of point guard Rajon Rondo isn't nearly as clear cut.

The Mavs claim Rondo has a back injury, but speculation persists that the disgruntled veteran was essentially banished. The cloud over the franchise was obvious.

"It's been a strange couple of days for this franchise," Nowitzki said before Game 3. "But when you're down and stuff is not really going right, you focus on yourself and what you have to do to get ready to play. You focus on the guys that are here."

The Rockets jumped out to a 12-point lead in the first quarter behind Harden and forward Terrence Jones, who both reached double-figure scoring early.

Dallas closed the gap by the end of the period, tied it early in the second and inched ahead 50-49 on center Tyson Chandler's dunk midway through the quarter.

The Mavs, on the strength of a 13-0 run, led by as much as 13 before settling into a 72-65 advantage at the break.

NOTES: Dallas announced that PG Rajon Rondo left the team to deal with a back injury that occurred in Game 2. Coach Rick Carlisle acknowledged that Rondo, a free agent this summer who clashed with Carlisle at times this season, likely won't ever play for the Mavericks again. "It's time to move on," Carlisle said. PG Raymond Felton started Game 3. ... Mavs F Chandler Parsons (knee) has been ruled out for the rest of the playoffs and is exploring surgical options. ... Houston C Dwight Howard played 33 minutes in Game 2, the most playing time he has seen since Jan. 19. ... Dallas G Devin Harris (toe) returned after missing the series' first two games.